Question

Let f(x) = 3x+1 and g(x) = x2
Part 1 [2 points] Find f(g(x))
Part 2 [2 points] Find g(f(x))
Part 3 [4 points] Use complete sentences to explain any difference in part 1 and part 2.

Answer 1

plug in x2 into f(x)
so 3(x2) + 1

Answer 2

\[f(g(x))=f(x^2)\] and since
\[f(\spadesuit)=3\spadesuit +1\] you have
\[f(x^2)=3x^2+1\]